I am trying to find the 'optimal' amount of a certain medicinal cream to be applied to a patient in order to minimize the days the patient has a rash. However, the data for the cream doses are of the values 0, 0.25, 0.5, 0.75, and 1 (on some scale, e.g., 50 milliliters). I am trying to build a regression model using these discrete values and find the optimal value on a continuous scale (i.e. outside these discrete values, [the optimal amount of cream to be applied could be 0.37]). I would also like to be able to predict the number of days a patient has a rash based on a continuous medicinal cream dose input (e.g., if a dose of 0.65 was applied, the patient would have a rash for 4 days)
At present, I am performing regression analysis suitable for continuous dependent variables e.g. lasso regression. Then using the model I have built, I am predicting the number of days a patient has a rash for, using a continuous input to 2 decimal places [0,0.01, 0.02, .... 0.98, 0.99, 1] a large number of times to see which consistently produces the lowest number of rash days.
I am unsure if this is the right approach any confirmation/guidance would be greatly appreciated.